Variance SS3 Further Mathematics Lesson Note

Introduction

The assumed mean and coded factor for finding the variance and standard deviation.

When the numbers in data are large, it may be difficult to compute the large numbers, Hence, A method to reduce the labour may need to be introduced to reduce it, and an assumed mean and coded method may be introduced. The following methods can be applied.

A = assumed mean

d = Deviation of assumed mean from the items = x – A From our earlier form 

 Suppose   

Then, X = A +  𝑑̅

Therefore our deviation from the mean becomes.

X =  𝑥̅ = d –  𝑑̅

 Standard deviation =  

When the coded factor is further introduced it becomes.

Variance = C

Standard deviation = C

 Example: The data below is that of the shoe sizes of 100 men for the NYSC.

Calculate for the data, the; 

1. Variance,
2. Standard deviation. 

       Class-Work.

The table below shows the transport allowance paid to 50 senior staff of a computer manufacturing company.

Calculate the data from the

1. Arithmetic mean using an assumed mean of #1025 
2. Variance.
3. Standard deviation.    

 Assignment.

The weights in Kg of 200 newborn babies in a local government are given as shown in the table below;

Using an assumed mean of 55 kg, Calculate the mean Variance and Standard deviation for the data.